What is the measure of an exterior angle of a regular nonagon?
Polygons are many-sided figures, with sides that are line segments. The most familiar polygons are the triangle, the rectangle, and the square. A regular polygon is one that has equal sides. Similarly, a regular nonagon is a 9-sided polygon with sides and angles equal. Let's find out the measure of an exterior angle of a nonagon.
Answer: The measure of an exterior angle of a regular nonagon is 40 degrees.
Let's understand the solution.
By using the formula (n - 2) × 180 / n, we can find the measure of an interior angle of a regular polygon.
Therefore, by substituting n = 9 to the above formula, we get 140 degrees.
Also, we know that: interior angle + exterior angle = 180 degrees
Therefore, we get the measure of an exterior angle by the above formula, that is, 180° - 140° = 40 degrees.
Hence, the measure of an exterior angle of a regular nonagon is 40 degrees.